Coaxial conductor system



Dec. 5, 1933. E, GREEN 1,937,652

coAxIAL CONDUCTOR SYSTEM Filed April 9, 19:51

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5'2- Coaxz'al Conductors Cons ta//ztw/edance CLU-v es Bahn/zetel'. I'tL'o US eccent/-L'cz'zf 5.0. .showing armenia/lucent w a'ameter Ratio, :Rx 9 P L7 INVENTOR Z GI/e/a/ BY M ATTORNEY Patented Dec. 5, 1933 1,937,652 coAirIAL CONDUCTORY SYSTEM Estill I. Green, East Orange, N. J., assignorfto VAmerican Telephone and Telegraph Company,

a corporation of New York VApplication April 9, 1931. serial No. 528,929

7 claims. (cl. rvs-44) This invention relates to coaxial conductor systems, and more particularly to arrangements for connecting or terminating coaxial conductor systems of different sizes and of different eccen- :ptricities without introducing impedance irregularities. v

4In the patent of E. I.y Green, No'. 1,841,493, granted January 19, 1932, the relation -of the characteristic impedance oi the coaxial con- 10 vductor system to the ratio of the diameters of the conductors is developed. In said application it is shown how this relationshipwmay be taken advantage of to join two concentric conductorsystems of different sizes without impedance irregularity. The invention of saidnapplication, however, involved the assumption that the concentric conductor was truly concentric, vthat is, there was no eccentricity of the conductors.

;v The present invention involves thev further fact that the impedance of a concentric conductor system is also a function of the eccentricity lof the conductors, the eccentricitybeing defined as the ratio of the distance between the centers of the two conductors to the inner radius of: the outer conducton Thus, it will be seen that we have two variables upon which the characteristic impedance depends: (1) the ratio between the inner diameter of the outer conductor and the outer diameter ofthe inner conductor and (2)y the eccentricity. By varying either or both of these factors a` concentric conductor system may be givenvany desired characteristic impedance. If two' concentric conductor systems of different ytypesiare to be connectedY together without impedance irregularity, either variable of either or both circuits may be Achanged sol that-the characteristic impedances of both circuits will be the same.

As a practical matter it will generally be found that the eccentricity of the circuit is to be'xed by certain structural considerations, and adjustments to obtain any desired impedance can be most vpractically Ymade by variationof the di- Aameter ratio. `For example,4 if two circuits of different Sizes are to be joined together, it will generally be found that the eccentricity of the smaller circuit will be more pronounced than for the larger circuit. So, also, where a section of concentric conductor` is curved, a certain amount of eccentricity may be introduced. This eccentricity in any sectiorrmay be taken care of by varying the diameter ratio of the two conductors of either the more eccentric section or the less. eccentric section to which it is to be joined.

The invention will nowbe more fully understood from the following description, when read in connection with the accompanying drawing in which Figure 1 shows how two sections of concentric conductor of diierent sizes and eccentricities may be joined, Fig. Zbeing avsectional diagram illustrating particularly what is meant by eccentricity, and Fig. 3 being a series of curves showing the relationship of the impedance to the two variable factors of eccentricity and diameter ratio.

Referring to Fig. y1, 1G designates the outer cylindrical conductor of a large concentric conductor section and 12 designates'the inner concentric ccnductor of the section. The two conductors are spaced by dielectric rings or spacers such as Shown at 14 and which may De strungalong the conductors at suitable intervals to give the necessary mechanical strength. Similarly, 1G and 12 designate the outer and inner ccnductors of another section of concentric conductor separated by spacers such as 14. This last mentioned concentric conductor section is .of smaller size than the sections shown at the conical unions 16 and 18 screwed to the ends of the conductors, as shown. The inner conductors 12and l2 may, if desiredbe solid w of hollow*V tubes as shown.

The characteristic impedance of a coaxial circuit varies with the ratio between the diameters ofthe two conductors and also with the eccentricity-of the circuit, the eccentricity being cusires instead f tomarily denedas the ratio of the distance between the centers of the two conductorspto the inner radius of the outerY conductor,

Thus, re-

ferring to Fig. 2 of the attached drawing, the

eccentricity is 'given by the ratio Let us consider vthe nature of the dependence of the coaxial circuit impedance upon each of these variables.

The impedance of a coaxial y circuit at high frequencies is given bythe expression 2 where L=the inductance per unit length, and C- the capacity per unit length. For perfect centering, the capacity C is:

.08941 :1o-ga? Inf. per mile while the inductance for no eccentricity is given by:

C Y u E milli-henries per mile L=.321910gc 3) where c is the inner radius of the outer conductor,

and b is the outer radius of the inner conductor. These formulas may be obtained from 'pages .72 and 109 of Calculation of Alternating Current Problems by L. Cohen.

Substituting these values for L and C in (l),

we find the familiar expression for the approxi-V mate impedance at high frequencies with no eccentricity as follows:

Let us now consider the eiect of eccentricity upon impedance. Referring to Alternating Currents by A. Russell, vol. I, page 166, We

that:

C=cm mf. per mile (5) COS Zbc This formula may be rewritten as follows:

10 1 b 1 e 2C mf. per m1e(6) 1 cosh [2 b+2 c 2(0)111 l showing that it involves only the two variables of eccentricity and diameter ratio constant is: n j

If C is now given the value indicated by 6), we ind from the constant velocity assumption that'the value of L is:

while the value of the high frequency impedance `Thus the Value ofyZo is given in terms of the two variables of diameter ratio and eccentricity. Fig. 3 of the attached drawing indicates a range of Vvariations, in thehigh frequency impedance due to these two variables, a number of curves tions.

of equal high frequency impedance beingplotted against the coordinates of diameter ratio and Y eccentricity.

Apedance upon the eccentricity and diameter ratios` suggests that inany section of line where the eccentricity must for any reason differ from the eccentricity in the adjoining section, an impedance irregularity may be avoided by choosing theV proper diameter ratios for the two sec- Thus, referring toFig. 3 of the drawing, 'a circuit witha diameter ratio of 3.90 and an eccentricityof 16 per cent is seen to have the same impedance (S0 ohms) as a circuit with a Where it isdesired to connect the two sections ofy concentricl conductor as shown in Fig. `1, the diameter ratio or the eccentricity of one'of the conductorsections or both may be varied to give the conductor sections any desired characteristic impedance and both characteristic lmpedances may, ofcourse, be made the same so that the two sections may be joined without impedance irregularity.

Differences in eccentricity at different parts of the line may result from the constructional requirements. Changes in the dimensions of the circuit would very likely be one ofthe principal causes of changes in eccentricity. While the clearances and tolerances necessary for the conductors and insulators may be smaller for a small coaxial `circuit than vfor a largeY one, nevertheless the ratio of these clearances and tolerancesto the circuit dimensions will be greater in the case of the smaller circuit. Hence a small coaxial circuit must in general have much greater eccentricity than a large one,A andthe proposal is to oiset this by adjusting the diameter ratio' as discussed above.'y Other causes of differences in' eccentricity for different line sections mightbe the use of curved construction in some sections, ilexible construction in others,

etc.

Since in a practical case the situation will be usually lone in which one of the conductor sectiens hasa certain amount of eccentricity which is xedby structuralconditions and the other section has little or noV eccentricity, the desired impedance values will usually be obtained by adjustment of the diameter'ratio of one of the conductor sections, rusually the one whose conductors 'are eccentric. In general, veccentricity of the conductors is undesirable and the necessary equality of impedance would not ordinarily be obtained in practice by varying the eccentricity. Y

In the aforementioned patent of E. I. Green, No. 1,841,473 a method is given for obtaining the same high frequency impedance in two coaxial conductor sections both of which have perfect concentricity, the dielectric constant of the insulating medium diifering, however, for the two' sections. The high frequency characteristic imwhere K is the weightedy average dielectric constant of the insulating material. If now we iis have two sections of coaxial circuit for .which the dielectric constantk differs and which have different amounts of eccentricity, the high frequency characteristic impedance of either section will be 1 1 c 1 b 1 e 2 c Za-Ow/COSII (c) (11) Suppose that it is desired under these conditions to secure the same impedance in the two sec-l tions. Usuallythe choice of insulating material and the amount of eccentricityvwill be dictated by physical considerations, so that the desired result may be most easily obtained by properly adjusting the diameter ratios in the two sections in accordance with Equation 11.

It will be obvious that the general principles herein disclosed may be embodied in many other organizationswidely different from those illustrated without departing from the spirit of the invention as defined in the following claims.

What is claimed is:

1. In a transmission system, two conductor sections each comprising cylindrical `conductors arranged one within the other, and the characteristic impedance of each section being a function of two physical characteristics of the section, (a)

the eccentricity of the conductors and (h) the ratio of their diameters, one said physical `characteristic of one of the sections being so related to the other physical characteristic of said section that both sections will have substantially equal characteristic impedances, and means for interconnecting said sections.

2. In a transmission system, two conductor sections each comprising cylindrical conductors arranged one within the other, and the characteristic impedance of each section being al function of two physical characteristics of the section, (a.) the eccentricity of the conductors and (b) rthe ratio of their diametersthe diameter ratio of one of the sections being so related to the eccentricity of the section that both sections will have substantially equal characteristic impedances, and l at highfrequencies is substantially the same for Y each section.

4. In a transmission system, two adjacent line sections each comprising two separate conductors arranged one inside the other, the conductors in the two line sections having different amounts of eccentricity, the dielectric constant of the insulating material being different for the two sections and the diameter ratios of the two sections being such that the characteristic impedance at high frequencies is substantially the same for each section. Y

5. In a transmission system, two conductor sections each comprising two cylindrical conductors arranged one inside thev other, the `values of the dielectricconstant of the insulating medium, the ratio of the inner radius of the outer conductor to the outer radius of the inner conductor, and the ratio of the interaxial separation of the inner and outer conductors to the inner radius of the outer conductor ineach of said sections being such that both sections will have substantially equal characteristic impedances at high frequencies.

6. In a transmission system, two conductor sections each comprising two cylindrical conductors arranged one .inside the other,y the values ofthe dielectric constant of the insulating medium, the inner radius of the outer conductor, the outer radius of the inner conductor, and the interaxial separation of the inner and outer conductors in each of said sections being such that both sections will have substantially equal characteristic impedances. f y

7. In a transmission system, two conductor sections each comprising two cylindrical conductors arranged one inside the other, the values of the dielectric constants of the insulating media, the inner radii of the outer conductors, the outer radii of the inner conductors, and the interaxial separations of the inner and outer conductors in said sections being related in `accordance with the formula where`K1, b1, c1, and el are, respectively, the dielectric constant of the insulating medium, the outer radius of the inner conductonthe inner radius of the4 outer conductor, and the interaxial,

separation of the inner and outer conductors in one of said sections, and K2, b2, c2, and e2 are the corresponding quantities inthe other of said sections.

' l ESTILL I. GREEN.

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